Quantitative Economics, Volume 4, Issue 3 (November 2013)

Abstract

This paper considers fixed effects estimation and inference in linear and non-linear panel data models with random coefficients and endogenous regressors.The quantities of interest—means, variances, and other moments of the randomcoefficients—are estimated by cross sectional sample moments of generalizedmethod of moments (GMM) estimators applied separately to the time series ofeach individual. To deal with the incidental parameter problem introduced by thenoise of the within-individual estimators in short panels, we develop bias correc-tions. These corrections are based on higher-order asymptotic expansions of theGMM estimators and produce improved point and interval estimates in moder-ately long panels. Under asymptotic sequences where the cross sectional and timeseries dimensions of the panel pass to infinity at the same rate, the uncorrectedestimators have asymptotic biases of the same order as their asymptotic standarddeviations. The bias corrections remove the bias without increasing variance. Anempirical example on cigarette demand based on Becker, Grossman, and Murphy(1994) shows significant heterogeneity in the price effect across U.S. states.Keywords. Correlated random-coefficient model, panel data, instrumental vari-ables, GMM, fixed effects, bias, incidental parameter problem, cigarette demand.JEL classification. C23, J31, J51.